IIRC the ltsp-client package in debian/ubuntu combines multiple techniques like usb forwarding, remote desktop connection, sound forwarding, etc.. There is no meta package like that in tinycore. But you can e.g. use x2goclient, which tries to accomplish the same (rdp+sound+disks), or use a combination of remmina (remote desktop) and fuse+sshfs for files and pulseaudio for sound serving.